Ex 6.3,21
Find the equation of the normal to the curve = 3 +2 +6
which are parallel to the line +14 +4=0.
Let , be the point on the Curve at which Normal is to be taken
Given Curve is
= 3 +2 +6
Since point , is on the Curve
, will satisfies the Equation of Curve
Putting = , =
= 3 +2 +6
= 3 +2 +6
We know that
Slope of a tangent to the Curve is
= 3 +2 +6
Differentiating w.r.t.
=3 2 +2
Since tangent to be taken from ,
Slope of tangent at , is
, =3 2 +2
We know that
Slope of tangent Slope of Normal = 1
3 2 +2 Slope of Normal = 1
Slope of Normal = 1 3 2 + 2
Also,
Given that Normal is parallel to the line +14 +4=0
If two lines are parallel then slopes are equal
Slopes of Normal = Slope of line +14 +4=0
Now, line is
+14 +4=0
14 = 4
= 4 14
= 1 14 4 14
The above equation is of the form = + where m is slope
Slope of line +14 +4=0 is 1 14
Now,
Slope of Normal = Slope of line +14 +4=0
1 3 2 + 2 = 1 14
1 3 2 + 2 = 1 14
14=3 2 +2
2 +2=14
3 2 =14 2
3 2 =12
2 = 12 3
2 =4
= 4
= 2
Finding equation of normal